Brain Organization and Computation Andreas Schierwagen Institute for Computer Science, Intelligent Systems Department, University of Leipzig, Leipzig, Germany [email protected]http://www.informatik.uni-leipzig.de/~schierwa Abstract. Theories of how the brain computes can be differentiated in three general conceptions: the algorithmic approach, the neural infor- mation processing (neurocomputational) approach and the dynamical systems approach. The discussion of key features of brain organization (i.e. structure with function) demonstrates the self-organizing character of brain processes at the various spatio-temporal scales. It is argued that the features associated with the brain are in support of its description in terms of dynamical systems theory, and of a concept of computation to be developed further within this framework. 1 Introduction The brain as the basis of cognitive functions such as a thinking, perception and acting has been fascinating scientists for a long time, and to understand its operational principles is one of the largest challenges to modern science. Only recently, the functional architecture of the brain has gained attention from scientific camps which are traditionally rather distant from neuroscience, i.e. from computer and organization sciences. The reason is that information technology sees an explosion of complexity, forming the basis for both great expectations and worries while the latter come up since software technology is facing a complexity bottleneck [1]. Thus various initiatives started to propa- gate novel paradigms of Unconventional Computing such as IBM’s ‘Autonomic Computing’ 1 , the ‘Grand Challenges in Computing Research’ in the UK 2 , and DFG’s ‘Organic Computing’ (DFG = German Science Foundation) 3 . According to current views, the brain is both a computing and organic en- tity. The research initiatives mentioned before see therefore the neurosciences as sources of concepts relevant for the new, unconventional computing paradigms envisioned. Hence, the formal concepts which were developed within the The- oretical Neuroscience to describe and understand the brain as an information processing system are of special relevance. This paper is organized as follows. Section 2 reviews some key features of brain organization (i.e. structure with function). It is followed by Section 3 1 http://www.research.ibm.com/autonomic 2 http://www.ukcrc.org.uk/grand challenges 3 http://www.organic-computing.org J. Mira and J.R. ´ Alvarez (Eds.): IWINAC 2007, Part I, LNCS 4527, pp. 31–40, 2007. c Springer-Verlag Berlin Heidelberg 2007
Transcript
Brain Organization and Computation
Andreas Schierwagen
Institute for Computer Science, Intelligent Systems Department, University ofLeipzig, Leipzig, Germany
Abstract. Theories of how the brain computes can be differentiated inthree general conceptions: the algorithmic approach, the neural infor-mation processing (neurocomputational) approach and the dynamicalsystems approach. The discussion of key features of brain organization(i.e. structure with function) demonstrates the self-organizing characterof brain processes at the various spatio-temporal scales. It is argued thatthe features associated with the brain are in support of its description interms of dynamical systems theory, and of a concept of computation tobe developed further within this framework.
1 Introduction
The brain as the basis of cognitive functions such as a thinking, perception andacting has been fascinating scientists for a long time, and to understand itsoperational principles is one of the largest challenges to modern science.
Only recently, the functional architecture of the brain has gained attentionfrom scientific camps which are traditionally rather distant from neuroscience,i.e. from computer and organization sciences. The reason is that informationtechnology sees an explosion of complexity, forming the basis for both greatexpectations and worries while the latter come up since software technology isfacing a complexity bottleneck [1]. Thus various initiatives started to propa-gate novel paradigms of Unconventional Computing such as IBM’s ‘AutonomicComputing’ 1, the ‘Grand Challenges in Computing Research’ in the UK 2, andDFG’s ‘Organic Computing’ (DFG = German Science Foundation) 3.
According to current views, the brain is both a computing and organic en-tity. The research initiatives mentioned before see therefore the neurosciences assources of concepts relevant for the new, unconventional computing paradigmsenvisioned. Hence, the formal concepts which were developed within the The-oretical Neuroscience to describe and understand the brain as an informationprocessing system are of special relevance.
This paper is organized as follows. Section 2 reviews some key features ofbrain organization (i.e. structure with function). It is followed by Section 31 http://www.research.ibm.com/autonomic2 http://www.ukcrc.org.uk/grand challenges3 http://www.organic-computing.org
Fig. 1. Levels of brain organization and methods for its investigation. This figure relatesthe resolution in space and time of various methods for the study of brain function(right) to the scale at which neuronal structures can be identified (left). Adaptedfrom [4]. MEG=magnetoencephalography; EP=evoked potentials; fMRT=functionalmagnetic resonance tomography; PET=positron emission tomography.
which discusses the different computational approaches developed in Theoretical(Computational) Neuroscience. Questions raised there include the search for thecomputational unit, the concept of modularity and the development of dynami-cal systems approaches. We end in Section 4 with some conclusions concerningthe needs of a theory of analog, emergent computation.
2 Brain Organization and Methods for Investigation
Neuroscientific research is practiced at very different levels extending from mole-cular biology of the cell up to the behavior of the organism. In the first line, natu-rally, the neuroscientific disciplines (Neuroanatomy, -physiology, -chemistry and-genetics) are involved, but also Psychology and Cognitive Science. TheoreticalNeurobiology (with its subdivisions Computational Neuroscience and Neurocom-puting), Physics and Mathematics provide theoretical contributions (e.g. [2,3]).The integration of the results gathered by the disciplines is expected to provideinsights in the mechanisms on which the functions of neurons and neural net-works are based, and in the long run in those of cognition. The well-groundedand efficient realization of this integration represents one of the greatest chal-lenges of actual neurosciences. New techniques like patch clamp, multi-electroderecording, electroencephalogram (EEG) and imaging methods such as mag-netoenzephalography (MEG), positron emission tomography (PET) and func-tional magnetic resonance tomography (fMRT, nuclear spin tomography) enable
Brain Organization and Computation 33
investigations on different system levels (Fig. 1), raising again the question ofhow to integrate conceptionally the results.
The human brain has on the average a mass of 1.4 kg. According to differentestimations it contains 1011 − 1012 neurons which differ from other cells of theorganism by the pronounced variability of their shapes and sizes (Fig. 2). The in-dividual morphologic characteristics of the neurons are important determinantsof neuronal function [5,6,7,8,9], and thus they affect the dynamic characteristicsof the neural network, to which they belong, either directly, or by specifying theentire connectivity between the neurons. In neural systems the influences are mu-tual, so that in general also the global network dynamics affect the connectivityand the form of the individual constituent neurons [5,10].
Fig. 2. Examples of dendritic neurons. Dendrites exhibit typical shapes which areused for classification of neurons. A. Purkinje cell from guinea pig cerebellum, B. a-motoneuron from cat spinal chord, C. spiny neuron from rat neostriatum, D. Outputneuron from cat superior colliculus. Figures A.-C. from [11], D. from [12].
The specific functions of the brain are essentially based on the interactionseach of a large number of neurons by means of their synaptic connections. Amammalian neuron supports between 104 and 105 synapses whose majority islocated on the dendrites. Estimations of the total number of synaptic connec-tions in the human brain amount to 1015. Depending on the effect upon thesuccessor neurons connections are classified as excitatory and inhibitory. Theneurons of the cortex are usually assigned to two main categories: the pyramidalcells with a portion of ca. 85%, and the stellate cells with ca. 15% [13]. Pyrami-dal neurons often have long-range axons with excitatory synapses, and stellatecells with an only locally branched axon often act in an inhibitory manner. The
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activation status of the pyramidal neurons possibly encodes the relevant infor-mation, while the stellate cells raise the difference between center and surroundby their inhibitory influence on the local environment, i.e. by lateral inhibition.
On the basis of distribution, density and size of the neuron somata the cortexcan be divided in six layers (e.g. [14]). The cell bodies of the pyramidal cellsparticularly are in the layers III–V, and their apical dendrites extend into theupper layer I. The somata of the stellate cells are mainly in the middle layers III–IV (see (Fig. 3). Efferent connections from the cortex to subcortical and otherstructures are formed by the axons of the pyramidal cells in layer V; afferencesto the cortex mainly come from the thalamus.
Hubel and Wiesel’s landmark studies [15,16] of the visual system have ledto the assumption that information processing in the brain generally follows ahierarchical principle. Important for the conceptional view on the function ofthe brain is, however, that there is also a multitude of feedback connections or‘back projections’, which e.g. in the geniculate body (CGL) by far outnumberthe forward connections. Nearly all brain regions influence themselves by theexistence of such closed signal loops [17]. This also applies to the function ofthe individual neurons, which are involved in signal processing within an areaor a subsystem of the brain. Further operational principles are divergence andconvergence of the connections, i.e. a neuron and/or an area sends its signalsto many others, and it also receives signals from many other neurons and/orareas. On the average, any two neurons in the cortex are connected by onlyone other neuron (‘two degrees of separation’, cf. [18]). This structurally causedfunctional proximity means in the language of information processing that thebrain is characterized through massive parallelism.
3 Computational Approaches
Theories of how the brain functions as an informational system are in differentways related to the levels of brain organization. We can differentiate three gen-eral conceptions : the algorithmic approach, the neural information processing(neurocomputational) approach and the dynamical approach [19].
The algorithmic computation approach attempts to use the formal definitionof computation, originally proposed by Turing [20] in order to understand neuralcomputation. Although brains can be understood in some formal sense as Turingmachines, it is now generally accepted that this reveals nothing at all of how thebrain actually works [19]. Thus, Turing’s definition of computation cannot bestraightly applied (e.g. [21]).
The neurocomputational approach was launched in 1988 by Sejnowski, Kochand Churchland [4]. By stressing the architecture of the brain itself Computa-tional Neuroscience was defined by the explicit research aim of “explaining howelectrical and chemical signals are used in the brain to represent and process in-formation”. In this approach, computation is understood as any form of processin neuronal systems where information is transformed [22]. The ‘acid test’ forthis approach (not passed as yet) is to find a definition for transformation of
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Fig. 3. Scheme of a neuronal circuit in the cerebral cortex. Pyramidal neurons (P —black triangles) receive inputs (either directly via afferent fibers, or from local neurons),generate outputs, and interact with one another. Local neurons (black circles — varioustypes of stellate cells) may be excitatory (E — empty synapse symbols) or inhibitory (I— black synapse symbols). Cortex layers are indicated on the left. Significant variationsin cell density, dendritic architecture, and synaptic arrangement enable a vast numberof computational possibilities.
information, such that not almost all natural systems count as computationalinformation processors [23,24].
The dynamical approach rests on concepts and theories from the sciences(Mathematics, Physics, Chemistry and Biology), and particularly from (Non-linear) Dynamical Systems Theory. It seeks to understand the brain in termsof analog, rate-dependent processes and physics style models. The brain is con-sidered as a large and complex continuous-time (often also continuous-space)physical system that is described in terms of the dynamics of neural excitationand inhibition.
3.1 Neurocomputational Concepts
While current neurocomputational concepts are of great diversity, most of themare tightly linked to the algorithmic view. The algorithmic as well as the neu-rocomputational approach attempt to explain properties of the nervous sys-tem (e.g., object recognition) in terms of parts of the system (cardinal cells,or ‘grandmother neurons’), in accordance with the decomposition principle of(linear) Systems Theory. Models of this kind seek to understand on a detailedlevel how synapses, single neurons, neural circuits and large populations processinformation. If the information processing capacity of the brain is compared inthis way with that of an algorithmic computer, one is confronted with severalproblems. In the first line, the units of computation are to be determined. Theidentification of the computational elements, however, is highly controversial.
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As is generally known, McCulloch and Pitts in their now classical work [25] de-fined the neuron as the basic computational unit, since they believed it were thesimplest nonlinear element.
Yet today it is obvious that (nonlinear) neuronal computation happens alreadyat subcellular scales (dendritic subunits, synaptic sites), possibly even in supra-molecular structures in dendrites. [26,27,28]. Correspondingly, e.g. synapses ascomputational units were analyzed in theoretical studies (e.g. [29]). But theproblem of the computational unit at these scales remains open [30].
Computational units are assigned to supracellular scales, too. Based on ideasintimately related to the decomposability principle underlying the algorithmicapproach, the principle of the modular organization of the brain has been formu-lated. According to this principle, the nervous system is composed of ‘buildingblocks’ of repetitive structures. The idea became known as the hypothesis of thecolumnar organization of the cerebral cortex; it was developed mainly after theworks of Mountcastle, Hubel and Wiesel, and Szenthagothai (for reviews, seee.g. [31,32,33]).
Referring to and based on these works, the spectacular Blue Brain Project wasstarted very recently. According to self-advertisement, the “Blue Brain projectis the first comprehensive attempt to reverse-engineer the mammalian brain, inorder to understand brain function and dysfunction through detailed simula-tions” [34]. The central role in this project play ‘cortical microcircuits’ whichhave been suggested as modules computing basic functions. Indeed, impressiveprogress has been made in developing computational models for defined ‘canon-ical’ microcircuits, especially in the case of online computing on time-varyinginput streams (see [35] and references therein).
It should be noted, however, that the concept of columnar organization hasbeen questioned by neurobiological experts. Reviewing new findings in differentspecies and cortical areas, it was concluded that the notion of a basic uniformityin the neocortex, with respect to the density and types of neurons per columnis not valid for all species [36]. Other experts even more clearly state that it hasbeen impossible to find a canonical microcircuit corresponding to the corticalcolumn [37]. These authors reason that although the column is an attractiveidea both from neurobiological and computational point of view, it has failed asan unifying principle for understanding cortical function.
3.2 Concepts from Dynamical Systems Theory
Inconsistencies between neurobiological facts and theoretical concepts are notnew in the history of Theoretical Neurobiology. In the case of the column con-cept they demonstrate that the decomposition principle is possibly not suitableto serve as exclusive guidance principle for the study of information processingin the brain. While the principle of decomposability has a great number of ad-vantages, for example just modularity, many problems in neuroscience seem notdecomposable this way. The reason is that brains (like all biological systems) areinherently complex.
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An appropriate framework for the description of the behavior of complexsystems is represented by the attractor concept of nonlinear dynamical systemstheory. Attractors may be informally defined as states of activity toward which asystem settles (relaxes) over time. The activity in a neural system is described bya trajectory in the high-dimensional state space, say RN where N is the numberof neurons. Since this state (or phase) space is continuous, the neural systemperforms an analog computation [38]. In this framework, a certain parametersetting (the initial condition) is interpreted as input, the attractor to whichthe system’s state flows as the output, and the flow itself as the process ofcomputation. The criteria of computational complexity developed for digitalalgorithms are not directly applicable to ‘analog algorithms’. Appropriate criteriaof ‘dynamic complexity’ have been suggested: the time of convergence to anattractor within defined error bounds, the degree of stability of the attractor, thepattern of convergence (asymptotic, or oscillatory), type of the attractor (static,periodic, chaotic, stochastic), etc. Important building blocks for a non-standardtheory of computation in continuous space and time have been developed bySiegelmann [39] by relating the dynamical complexity of neural networks withusual computational complexity.
While standard artificial neural networks have only point attractors, dynam-ical systems theory easily handles also cases where the output is a limit cycle ora chaotic attractor. The respective systems, however, have not been consideredin computational terms as yet. This holds also for the so-called active, excitableor reaction-diffusion media, of which continuous neural fields are instances (see[40]). These media — spatially extended continua — exhibit a variety of spatio-temporal phenomena. Circular waves, spiral waves, and localized mobile exci-tations (‘bumps’) are the most familiar examples. The challenge is to find outhow these phenomena can be used to perform useful computations. Generally,data and results are given by spatial defects and information processing is im-plemented via spreading and interaction of phase or diffusive waves. In severalstudies it was shown that these media have real capabilities to solve problemsof Computational and Cognitive Neuroscience (formation of working memory,preparation and control of saccadic eye movements, emergence of hallucinationsunder the influence of drugs or the like, ‘near-to-death’ experiences, for overviewsee e.g. [41,42] and the references therein) and Artificial Intelligence (navigationof autonomous agents, image processing and recognition, e.g. [43,44]).
4 Conclusions
During the last decade, useful insights on structural, functional and computa-tional aspects of brain networks have been obtained employing network theory[45,46]. From the many investigations in this area (see e.g. [47] for review) weknow that the complexity of neural networks is due not only to their size (numberof neurons) but also to the interaction of its connection topology and dynamics(the activity of the individual neurons), which gives rise to global states andemergent behaviors.
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Several attempts were made to substantiate the general idea of computationalsystems which acquire emergent capabilities during a process of self-organization.The holistic properties of self-organizing systems represent a central intricacy inthis respect. There is no ‘natural’ way to decompose such a system. If a decompo-sition is made anyhow (e.g. based on anatomical information only), subsystemsshould at first have a certain behavioral potential (i.e. multi-functionality). Ideasof the unfolding of multi-functionality were subsumed by Shimizu [48] under theterm relational system. Relational systems obtain their functional propertiesonly during mutual interaction with the other elements of the system while onits part the interactions of the elements depend on the evolving properties ofthe elements. Thus, an iterative process takes place which is based on princi-ples of self-reference and self-organization. The properties of the system as awhole emerge in such a way that it is able to cope with perturbations from theenvironment.
An attempt to formalize this concept was undertaken recently [49] using‘chaotic neuromodules’. The results obtained from applications to evolutionaryrobotics demonstrate the multi-functional properties of coupled chaotic neuro-modules but also the limitations of the linear couplings used [50].
A general conclusion to be drawn is that a great deal of progress in Theo-retical Neuroscience will depend on tools and concepts made available throughthe dynamical systems approach to computing. Steps to overcome the existingtheoretical restrictions in this area are essential not only for solving the problemsin the Neurosciences but also to reach the goals of Unconventional Computing.
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